I have the following Logistic model equation (left out the values for the constants for simplicity), which I'm unable to solve for $P(t)$.
$\dfrac {dP} {dt} = kP \left (1- \dfrac P {P_\infty} \right)-H$
If the harvesting constant, $H$ was not present, then the ODE could be solved by Bernoulli's equation. The problem is that I am not sure how to start solving this specific type of differential equation.
Can someone point me in the right direction?
Thank you for your time!
Best Answer
The equation is in separated variables: $$ \frac{dP}{k\,P \left (1- \dfrac P {P_\infty} \right)-H}=dt. $$